Question

The graph of g(x) is the graph of f(x)=x+6 reflected across the x-axis. Which equation describes the function g?

A. g(x)=x−6
B. g(x)=−x−6
C. g(x)=−6x−6
D. g(x)=−x+6

Answer 1

ANSWER

The correct answer is $g(x)=-x-6$

EXPLANATION

The mapping for reflection across the x-axis is given by $(x,-y)$

Given $f(x)=x+6$. We can let $y=x+6$

we can write the ordered pair $(x,y)$ or $(x,x+6)$ as the ordered pair of the preimage of $f$.

The image function will have the ordered pair $(x,-y)$

or

$(x,-x-6)$.

That is, we negate all the y-coordinates.

Therefore

$g(x)=-x-6$.

Answer 2

I took the test and this was the answer